Utilization Bounds for Multiprocessor Rate-Monotonic Scheduling

In this paper, we extend Liu and Layland's utilization bound for fixed priority scheduling on uniprocessors to homogeneous multiprocessor systems under a partitioning strategy. Assuming that tasks are pre-emptively scheduled on each processor according to fixed priorities assigned by the Rate-Monotonic policy, and allocated to processors by the First Fit algorithm, we prove that the utilization bound is (n–1)(2^1/2–1)+(m–n+1)(2^1/(m–n+1)–1), where m and n are the number of tasks and processors, respectively. This bound is valid for arbitrary utilization factors. Moreover, if all the tasks have utilization factors under a value , the previous bound is raised and the new utilization bound considering is calculated. Finally, simulation provides the average-case behavior.